Two-step empirical CDF from one-step empirical CDF

Suppose I have a random variable which changes by from one timestep to the next. Suppose I do an experiment where I observe values of $\delta_0$ and make an experimental CDF of , by sorting so that , and then approximating the CDF of as where $d_i \leq y \leq d_{i+1}$.

Question: What is the most efficient way to compute the empirical CDF of two steps of , assuming that the process for going from to follows the same empirical distribution? The brute force way that occurs to me is to create the set , sorting and then approximating the two-step CDF of as where .